Some Models For Intuitionistic Finite Type Arithmetic With Fan Functional

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Constructivism In Mathematics Vol 2

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Author : A.S. Troelstra
language : en
Publisher: Elsevier
Release Date : 2014-06-28

Constructivism In Mathematics Vol 2 written by A.S. Troelstra and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-28 with Mathematics categories.

Studies in Logic and the Foundations of Mathematics, Volume 123: Constructivism in Mathematics: An Introduction, Vol. II focuses on various studies in mathematics and logic, including metric spaces, polynomial rings, and Heyting algebras. The publication first takes a look at the topology of metric spaces, algebra, and finite-type arithmetic and theories of operators. Discussions focus on intuitionistic finite-type arithmetic, theories of operators and classes, rings and modules, linear algebra, polynomial rings, fields and local rings, complete separable metric spaces, and located sets. The text then examines proof theory of intuitionistic logic, theory of types and constructive set theory, and choice sequences. The book elaborates on semantical completeness, sheaves, sites, and higher-order logic, and applications of sheaf models. Topics include a derived rule of local continuity, axiom of countable choice, forcing over sites, sheaf models for higher-order logic, and complete Heyting algebras. The publication is a valuable reference for mathematicians and researchers interested in mathematics and logic.

Handbook Of Proof Theory

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Author : S.R. Buss
language : en
Publisher: Elsevier
Release Date : 1998-07-09

Handbook Of Proof Theory written by S.R. Buss and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-07-09 with Mathematics categories.

This volume contains articles covering a broad spectrum of proof theory, with an emphasis on its mathematical aspects. The articles should not only be interesting to specialists of proof theory, but should also be accessible to a diverse audience, including logicians, mathematicians, computer scientists and philosophers. Many of the central topics of proof theory have been included in a self-contained expository of articles, covered in great detail and depth.The chapters are arranged so that the two introductory articles come first; these are then followed by articles from core classical areas of proof theory; the handbook concludes with articles that deal with topics closely related to computer science.

Some Models For Intuitionistic Finite Type Arithmetic With Fan Functional

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Author : Anne Sjerp Troelstra
language : en
Publisher:
Release Date : 1974

Some Models For Intuitionistic Finite Type Arithmetic With Fan Functional written by Anne Sjerp Troelstra and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Modular arithmetic categories.

Applied Proof Theory Proof Interpretations And Their Use In Mathematics

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Author : Ulrich Kohlenbach
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-05-23

Applied Proof Theory Proof Interpretations And Their Use In Mathematics written by Ulrich Kohlenbach and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-05-23 with Mathematics categories.

This is the first treatment in book format of proof-theoretic transformations - known as proof interpretations - that focuses on applications to ordinary mathematics. It covers both the necessary logical machinery behind the proof interpretations that are used in recent applications as well as – via extended case studies – carrying out some of these applications in full detail. This subject has historical roots in the 1950s. This book for the first time tells the whole story.

Digital And The Real World The Computational Foundations Of Mathematics Science Technology And Philosophy

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Author : Klaus Mainzer
language : en
Publisher: World Scientific
Release Date : 2017-11-17

Digital And The Real World The Computational Foundations Of Mathematics Science Technology And Philosophy written by Klaus Mainzer and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-17 with Mathematics categories.

In the 21st century, digitalization is a global challenge of mankind. Even for the public, it is obvious that our world is increasingly dominated by powerful algorithms and big data. But, how computable is our world? Some people believe that successful problem solving in science, technology, and economies only depends on fast algorithms and data mining. Chances and risks are often not understood, because the foundations of algorithms and information systems are not studied rigorously. Actually, they are deeply rooted in logics, mathematics, computer science and philosophy.Therefore, this book studies the foundations of mathematics, computer science, and philosophy, in order to guarantee security and reliability of the knowledge by constructive proofs, proof mining and program extraction. We start with the basics of computability theory, proof theory, and information theory. In a second step, we introduce new concepts of information and computing systems, in order to overcome the gap between the digital world of logical programming and the analog world of real computing in mathematics and science. The book also considers consequences for digital and analog physics, computational neuroscience, financial mathematics, and the Internet of Things (IoT).

The Journal Of Symbolic Logic

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Author : Alonzo Church
language : en
Publisher:
Release Date : 1980

The Journal Of Symbolic Logic written by Alonzo Church and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with Electronic journals categories.

Includes lists of members.

Rewriting And Typed Lambda Calculi

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Author : Gilles Dowek
language : en
Publisher: Springer
Release Date : 2014-07-01

Rewriting And Typed Lambda Calculi written by Gilles Dowek and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-01 with Mathematics categories.

This book constitutes the refereed proceedings of the Joint 25th International Conference on Rewriting Techniques and Applications, RTA 2014, and 12th International Conference on Typed Lambda-Calculi and Applications, TLCA 2014, held as part of the Vienna Summer of Logic, VSL 2014, in Vienna, Austria, in July 2014. The 28 revised full papers and 3 short papers presented were carefully reviewed and selected from 87 submissions. The papers provide research results on all aspects of rewriting and typed lambda calculi, ranging from theoretical and methodological issues to applications in various contexts. They address a wide variety of topics such as algorithmic aspects, implementation, logic, types, semantics, and programming.

Mathematical Reviews

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Author :
language : en
Publisher:
Release Date : 2001

Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.

The Philosopher S Index

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Author :
language : en
Publisher:
Release Date : 2008

The Philosopher S Index written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Philosophy categories.

Vols. for 1969- include a section of abstracts.

Crossroads Of Computability And Logic Insights Inspirations And Innovations

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Author : Arnold Beckmann
language : en
Publisher: Springer Nature
Release Date : 2025-06-19

Crossroads Of Computability And Logic Insights Inspirations And Innovations written by Arnold Beckmann and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-19 with Computers categories.

This book constitutes the refereed proceedings of the 21st Conference on Computability and Logic, CiE 2025, held in Lisbon, Portugal, during July 14–18, 2025. The 27 full papers included in this book were carefully reviewed and selected from 49 submissions. They focus on computability-related science, ranging over mathematics, computer science and applications in various natural and engineering sciences, such as physics and biology, as well as related fields, such as philosophy and history of computing. CiE 2025 had as its motto Crossroads of Computability and Logic: Insights, Inspirations, and Innovations, drawing on the numerous interconnections between computability research and broader logical methodologies, considering both well-established perspectives as well as recent innovations.